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Simultaneous Stabilization of Linear Systems

  • Book
  • © 1994

Overview

Authors:
  1. Vincent Blondel
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Part of the book series: Lecture Notes in Control and Information Sciences (LNCIS, volume 191)

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Table of contents (6 chapters)

  1. Front Matter

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  2. Introduction

    Pages 1-14

  3. Stabilization

    Pages 15-45

  4. Youla-Kucera parametrization

    Pages 46-67

  5. Necessary conditions: Interlacement

    Pages 68-101

  6. Sufficient conditions: Special cases

    Pages 102-131

  7. Necessary and sufficient conditions: Rational decidability

    Pages 132-144

  8. Back Matter

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Keywords

About this book

Simultaneous Stabilization of Linear Systems is devoted to a single question from Linear Systems Theory: "When is it possible to find a controller that stabilizes a finite family of systems?", known as the Simultaneous Stabilization Question. This question is satisfactorily solved when the number of systems is limited to two but is open for three or more systems. This constitutes one of the important, longstanding open problems in Linear Systems Theory. Dr. Blondel reviews partial answers and discusses partial answers with equivalent formulations of the problem. Particular emphasis is placed on interlacement conditions. The parity and the interlacing conditions are presented in a clear and unified framework. The final chapter "proves" the latest research progress and shows that, contrary to most of the questions in Linear Systems Theory, there exists no necessary and sufficient conditions for simultaneous stabilization of three or more systems that involve only the coefficients of the systems and a combination of rational operations.

Bibliographic Information

  • Book Title: Simultaneous Stabilization of Linear Systems

  • Authors: Vincent Blondel

  • Series Title: Lecture Notes in Control and Information Sciences

  • DOI: https://doi.org/10.1007/3-540-19862-8

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag London 1994

  • Softcover ISBN: 978-3-540-19862-8Published: 01 December 1993

  • eBook ISBN: 978-3-540-39321-4Published: 15 August 2005

  • Series ISSN: 0170-8643

  • Series E-ISSN: 1610-7411

  • Edition Number: 1

  • Number of Pages: XXI, 188

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Control, Robotics, Mechatronics

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